Topological Properties of Hypercubes
IEEE Transactions on Computers
On the existence of Hamiltonian circuits in faulty hypercubes
SIAM Journal on Discrete Mathematics
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Parallel computation: models and methods
Parallel computation: models and methods
Fault-tolerant hamiltonian laceability of hypercubes
Information Processing Letters
Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes
Information Processing Letters
Fault-Hamiltonicity of Hypercube-Like Interconnection Networks
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Many-to-Many Disjoint Path Covers in Hypercube-Like Interconnection Networks with Faulty Elements
IEEE Transactions on Parallel and Distributed Systems
Path bipancyclicity of hypercubes
Information Processing Letters
Hamiltonian circuit and linear array embeddings in faulty k-ary n-cubes
Journal of Parallel and Distributed Computing
Cycles embedding in hypercubes with node failures
Information Processing Letters
Cycles passing through prescribed edges in a hypercube with some faulty edges
Information Processing Letters
Conditional edge-fault-tolerant edge-bipancyclicity of hypercubes
Information Sciences: an International Journal
Fault-free Hamiltonian cycles in crossed cubes with conditional link faults
Information Sciences: an International Journal
Edge-bipancyclicity of conditional faulty hypercubes
Information Processing Letters
Embedding of meshes in Möbius cubes
Theoretical Computer Science
Edge-bipancyclicity of a hypercube with faulty vertices and edges
Discrete Applied Mathematics
A fault-free Hamiltonian cycle passing through prescribed edges in a hypercube with faulty edges
Information Processing Letters
Edge-fault-tolerant Hamiltonicity of pancake graphs under the conditional fault model
Theoretical Computer Science
Embedding a family of 2D meshes into Möbius cubes
WSEAS Transactions on Mathematics
Edge-fault-tolerant bipanconnectivity of hypercubes
Information Sciences: an International Journal
Long paths in hypercubes with conditional node-faults
Information Sciences: an International Journal
Embedding Hamiltonian cycles in alternating group graphs under conditional fault model
Information Sciences: an International Journal
Fault-free longest paths in star networks with conditional link faults
Theoretical Computer Science
Some results on topological properties of folded hypercubes
Information Processing Letters
1-vertex-fault-tolerant cycles embedding on folded hypercubes
Discrete Applied Mathematics
Embedding fault-free cycles in crossed cubes with conditional link faults
The Journal of Supercomputing
Fault-Free Cycles in Conditional Faulty Folded Hypercubes
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
Fault-Tolerant Hamiltonicity of Augmented Cubes under the Conditional Fault Model
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
Embedding geodesic and balanced cycles into hypercubes
WSEAS Transactions on Mathematics
Path embedding on folded hypercubes
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Conditional edge-fault Hamiltonicity of augmented cubes
Information Sciences: an International Journal
Hamiltonicity of matching composition networks with conditional edge faults
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Pancyclicity and bipancyclicity of conditional faulty folded hypercubes
Information Sciences: an International Journal
Embedding of tori and grids into twisted cubes
Theoretical Computer Science
Mutually independent Hamiltonian cycles in dual-cubes
The Journal of Supercomputing
Conditional edge-fault-tolerant Hamiltonicity of dual-cubes
Information Sciences: an International Journal
Pancyclicity of ternary n-cube networks under the conditional fault model
Information Processing Letters
Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model
SIAM Journal on Discrete Mathematics
A note on cycle embedding in hypercubes with faulty vertices
Information Processing Letters
Mutually independent Hamiltonian cycles in k-ary n-cubes when k is even
Computers and Electrical Engineering
One-to-one disjoint path covers on k-ary n-cubes
Theoretical Computer Science
Embedding hamiltonian paths in k-ary n-cubes with conditional edge faults
Theoretical Computer Science
Regular connected bipancyclic spanning subgraphs of hypercubes
Computers & Mathematics with Applications
Edge-bipancyclicity of all conditionally faulty hypercubes
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
Geodesic pancyclicity of twisted cubes
Information Sciences: an International Journal
Fault-tolerant path embedding in folded hypercubes with both node and edge faults
Theoretical Computer Science
Fault-tolerant embedding of cycles of various lengths in k-ary n-cubes
Information and Computation
Fault-tolerant cycle embedding in the faulty hypercubes
Information Sciences: an International Journal
Hamiltonian cycles in hypercubes with faulty edges
Information Sciences: an International Journal
Paired many-to-many disjoint path covers in faulty hypercubes
Theoretical Computer Science
| Hi-index | 5.24 |
The n-dimensional hypercube Qn is a graph having 2n vertices labeled from 0 to 2n - 1. Two vertices are connected by an edge if their binary labels differ in exactly one bit position. In this paper, we consider the faulty hypercube Qn with n ≥ 3 that each vertex of Qn is incident to at least two nonfaulty edges. Based on this requirement, we prove that Qn contains a Hamiltonian path joining any two different colored vertices even if it has up to 2n - 5 edge faults, Moreover, we show that there exists a path of length 2n - 2 between any two the same colored vertices in this faulty Qn. Furthermore, we also prove that the faulty Qn still contains a cycle of every even length from 4 to 2n inclusive.